Express $x^2 + 6x + 10$ in the form $(x + p)^2 + q$, where $p$ and $q$ are constants to be found. Answer ------------------------------- Given that $y = x^2 + 6x + c$, make $x$ the subject of the formula. Answer -------------------------------

1. Rewrite the quadratic as a completed square and simplify the constant term.

$x^2+6x+10=(x+3)^2-9+10=(x+3)^2+1$

1. Complete the square for the quadratic expression in $x$.

$y=x^2+6x+c$

$y=(x+3)^2-9+c$

2. Isolate the squared expression involving $x$.

$(x+3)^2=y-c+9$

3. Take square roots and solve for $x$.

$x+3=\pm\sqrt{y-c+9}$

$x=-3\pm\sqrt{y-c+9}$